His name is Lucifer. That's it. Just Lucifer. Satan is Hebrew for "the Opposer. which is what he tries to do. He Tries and Fails at ever turn to Oppose The Father. So if he has a last name it would have to be. LOOOOSSSSEEEERRRR.

Applying the rule of opposites (my own subjective approach), I doubt he has a name. The redeemed are given an identity along with total discretion over it: "known only to them and to those whom they wish to make their name known." It's likely then that the damned are stripped of their identity and that Satan is purely a literary device to identify the architect of evil.